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\begin{titlepage}

\noindent
\begin{flushleft}
{\bf H1prelim-13-032} Submitted to    \\
\noindent\rule{20cm}{1.8pt}
{\bf XXI International Workshop on Deep-Inelastic Scattering and Related Subjects, DIS2013}, April 22-26, 2013, Marseille~~~~~~~~
Parallel Session~~~~~~~~~~~~{\bf QCD and Final States}\\
\noindent\rule{20cm}{1.8pt}
{\it Electronic Access: www-h1.desy.de/publications/H1preliminary.short\_list.html}
\end{flushleft}



\noindent
%Date:          [today  instruction is preferred] \\ %\today      \\
%Version:       0.99 (\today)\\%Preparatives 0.1,0.2...; 1st draft: 1.0, 1.1...; 2nd Draft 2.0..., Final Reading 3.0,3.1...      \\
%Editors:         Alexander Bylinkin, Andrey Rostovtsev   \\
%Referees:       Michael Steder, Dietrich Wegener    \\
%Comments by         \\
\noindent
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%%%%% {\it {\large version of \today}} \\[.3em]
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\vspace{2cm}
\begin{center}
\begin{Large}

{\bf Measurement of charged particle production in deep-inelastic {\boldmath $ep$ scattering at $\sqrt{s}=225$}GeV at HERA\\}%(version of \today )}

\vspace{2cm}

H1 Collaboration

\end{Large}
\end{center}

\vspace{2cm}

\begin{abstract}
Charged particle production is measured in deep inelastic ep scattering at $\sqrt{s}=225$~GeV with the H1 detector at HERA. The kinematic range of the analysis covers low photon virtualities,  $5 < Q^2 < 10$ GeV$^2$, and medium to high values of inelasticity $y, 0.35 < y < 0.8$. The analysis is performed in the virtual photon-proton centre-of-mass system. The charged particle production cross sections is investigated double-differentially as a function of pseudorapidity $\eta^*$ and transverse momentum $p_T^*$ in the range $0 < \eta^* < 3.5$ and $p_T^* < 10$ GeV. The data are compared to different phenomenological models.

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\newpage

\section{Introduction}
\par
Recently, it was found that the shape of charged particle transverse momentum distributions measured in baryon-baryon interactions is distinctly different from that observed in gamma-gamma interactions~\cite{OUR1}. This is an indication for possible differencee in underlying dynamics of hadron production for these two types of particle collisions. At HERA both photoproduction and DIS processes are mediated by photon exchange, and therefore it provides an unique possibility to study the intermediate case of baryon-photon interactions. Na\"ively one would expect to observe a change in the hadron production dynamics at central rapidities %of produced particles 
in photon-proton ($\gamma^*p$) centre-of-mass system.
\par
Due to the strong asymmetry in the beam energies of electron and proton beams %colliding photon and proton 
at HERA the previous inclusive hadron production measurements \cite{H1particle} %were made on the photon side of event rapidity space. 
had only limited access to the central rapidity region in the $\gamma^*p$ frame. This region can be studied more easily by using the data collected at
%In order to make such measurements close to the central rapidity values one has to run the experiment under much less asymmetric conditions, i.e. with 
reduced proton beam energy and by restricting the 
event kinematics  to large values of the $\gamma^*p$ rest mass $W_{\gamma^*p}$.
%with maximal possible energy of the exchange photon.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Event Selection}
\subsection{DIS and detector level selection}
In 2007 the HERA $ep$-collider has also been run at %nominal electron beam energy ($E_e=27.5$~GeV) and 
reduced proton beam energy ($E_p=460$~GeV) for three months in which the H1experiment has collected data  corresponding to an integrated luminosity of $12.45$~pb$^{-1}$. %under these beam conditions. 
These data %collected by the H1 experiment 
are used in the present analysis of the charged particle spectra shape %at central rapidity values 
in the  $\gamma^*p$ rest frame.
\par
DIS events are recorded using triggers based on electromagnetic energy deposits in the SpaCal calorimeter. The trigger efficiency is determined using independently triggered data. For DIS events the trigger efficiency is determined to be almost $100\%$ in the kinematic region of the analysis. The scattered lepton, defined by the most energetic SpaCal cluster, is required to have an
energy $E_e$ larger than $3.4~$GeV. The kinematical phase space is defined by $5 < Q^2 < 10~ $GeV$^2$ and $0.35 < y < 0.8$, corresponding to the geometric acceptance of the SpaCal.
\par
Several cuts are applied to suppress photoproduction background. 
The electron identification selection criteria are designed to have a high efficiency for the signal while rejecting significantly %amount of 
the background.
A detailed description of these cuts can be found elsewhere~\cite{FL}.
\subsection{Tracks Selection}
\par
The tracks used in the analysis are measured in the central tracking detector (CTD). 
The reconstruction in the central region is based on two drift chambers, CJC1 and CJC2. The tracks are used to define the event vertex. In this analysis only
 tracks from the primary vertex are considered.
\par
In order to provide a higher efficiency of the track reconstruction, the following cuts are applied:
\begin{itemize}
\item The transverse momentum $p_T$ of a track has to be larger than $0.12$ GeV.
\item The polar angular range of a track is required to be $20^\circ < \theta < 160^\circ$.
\item Tracks are required to have a radial length L (the radial distance between the first and the last hit) larger than $10$ cm for the full $\theta$ range to ensure good momentum resolution.
\item Starting point of a track is required to be in CJC1.
\end{itemize}

\subsection{Definition of experimental observables}
The results of this analysis are presented in the $\gamma^*p$ centre-of-mass frame, to minimise the effect of the transverse boost from the virtual photon. The transformation to the this frame is reconstructed with the knowledge of the  kinematic variables $Q^2$ and $y$. The transverse momentum and pseudorapidity of charged particles in this frame are labeled as $p^*_T$ and $\eta^*$. In the photon-proton centre-of-mass frame the pseudorapidity is defined as $\eta^* = \ln(\tan(\theta^*/2))$, where $\theta^*$ is the polar angle of the track with respect to the virtual photon direction, i.e. the positive $z^*$ direction. All hadronic final state particles with $\eta^* > 0 $ belong to the current hemisphere, and all particles with $\eta^*< 0$ are assigned to the target or proton remnant hemisphere.
\par
The transverse momenta of charged particles are studied in the pseudorapidity region $0 <\eta^* < 3.5$ which is divided into seven equal intervals. This division in $\eta^*$-intervals is made in order to investigate how the charged particle $p^*_T$-spectrum changes with  $\eta^*$ going form the photon direction to the central fragmentation region.%of produced particles is approaching the proton's half of the rapidity space in photon-proton centre-of-mass system. 
The target region, $\eta^* < 0$, is not accessible in this analysis.
The transverse momenta of charged particles is measured for $p_T^* > 150~$ MeV in order to minimize the influence of the boost to virtual photon-proton centre-of-mass frame.


\subsection{Cross Section Definition}

The double differential cross section is %standardly 
defined at Born level by the following equation
\begin{linenomath}
\begin{equation}
\label{eq.3}
\frac{{\rm d}^2\sigma}{d{\rm p}^{*2}_T{\rm d}\eta^*} = \frac{N_{sig}}{\mathcal{L}\cdot2p^*_T \cdot \Delta p^*_T \cdot \Delta \eta^* \cdot A \cdot \varepsilon_1 \ldots \varepsilon_n} \cdot RC
\end{equation}
\end{linenomath}
where $\mathcal{L}$ is the luminosity, $\Delta \eta^*$ and $\Delta p^{*2}_T ~ = ~2 \cdot p^*_T \cdot \Delta p^*_T$ are the bin widths, $\varepsilon_i$ is the efficiency of a given cut $i$, $A$ - the acceptance correction measured at the reconstructed level in the radiative Monte Carlo (with the initial and final state radiation turned on) to the cross section at the generator level: 
\begin{linenomath}
\begin{equation}
\label{eq.4}
A = \frac{N^{rad}_{rec}}{N^{rad}_{gen}},
\end{equation}
\end{linenomath}
and $RC$ is a radiative correction factor extracted using the ratio of the MC calculated cross section excluding initial and final state radiation to that with radiation included:
\begin{linenomath}
\begin{equation}
\label{eq.5}
RC = \frac{\sigma^{norad}_{gen}}{\sigma^{rad}_{gen}}.
\end{equation}
\end{linenomath}
\par
The bin-center correction is also performed assuming the points to lie in the geometrical centers of $p_T*$ bins. 
The DJANGOH MC was used to correct the data. 

\section{Results and Discussions}
The measured cross section ${\rm d}\sigma/{\rm d}\eta^*$ for charged particles with $p^*_T > 0~$GeV is shown %are measured 
 in  figure~\ref{figeta} together with the predictions  DJANGOH and RAPGAP  normalised to the data. The shape of the pseudorapidity distribution is described by Monte Carlo rather well.
\par
The double differential cross sections ${{\rm d}^2\sigma}/{d{\rm p}^{*2}_T{\rm d}\eta^*}$ for charged particles are shown in figure~\ref{figpt} together with the absolute predictions from DJANGOH and RAPGAP. 
The ratio MC over data is shown in figure~\ref{fig.rat} applying the same normalisation factors to the models predictions as used in figure~\ref{figeta} independently of $\eta^*$. %shows the ratios between MC and data normalised to the total number of events.  
Although these models provide a rather good description of the cross section in $\eta^*$ (figure~\ref{figeta}) they fail to describe the shape of the transverse momentum spectra of the charged particles (figure~\ref{fig.rat}).
\par
To study the hadroproduction dynamics we use the
approximation which has been proposed recently~\cite{OUR1}. This approach suggests 
that the shape of the particle production $p_T^*$ spectrum can be described %to describe the particle production spectra shape as function of the particles transverse momentum 
by the sum of an exponential (Boltzmann-like) and a power-law statistical distributions:
\begin{linenomath}
\begin{equation}
\label{eq.exppl}
\frac{{\rm d}\sigma}{p^*_T {\rm d} p^*_T} = A_e\exp {(-E_{Tkin}/T_e)} +
\frac{A}{(1+\frac{\displaystyle p_T^{*2}}{\displaystyle T^{2}\cdot N})^N},
\end{equation}
\end{linenomath}
where  $E_{Tkin} = \sqrt{p_T^{*2} + M^2} - M$
with $M$ equal to the produced hadron mass. $A_e, A, T_e, T, N$ are free parameters to be determined by fit to the data. For charged hadron spectra a hadron mass is assumed to be equal to the pion mass.
Detailed arguments for this particular choice are given in~\cite{OUR1} and a phenomenological explanation of the formula~(\ref{eq.exppl}) has been recently given in ~\cite{OUR2}. The parameterisation in equation (\ref{eq.exppl}) provides a much better description of the data than the one traditionally used~\cite{old_model}.
\par
 The double differential cross sections ${{\rm d}^2\sigma}/{d{\rm p}^{*2}_T{\rm d}\eta^*}$  are shown for seven $\eta^*$ bins in figure~\ref{fig} together with the fit~(\ref{eq.exppl}).
 
The relative contribution of the exponential and power-law terms of the approximation~(\ref{eq.exppl}) can be characterised by ratio $R$ of the power-law term alone to the parameterisation function integrated over $p_T^{2}$. The power-law term can be calculated in the following way:
\begin{linenomath}
\begin{equation}\label{eq:Pl}
\nonumber \int_{0}^{\infty}\frac{A}{(1 + \frac{\displaystyle p_T^{*2}}{\displaystyle T^2N})^N}{\rm d}p_T^{*2}= \frac{ANT^2}{N-1}.
\end{equation}
\end{linenomath}
The exponential:
\begin{linenomath}
\begin{eqnarray}%\label{eq:Exp}
\nonumber &&A_e\int_{0}^{\infty}e^{-\frac{\displaystyle E_{Tkin}}{\displaystyle T_e}}{\rm d}p_T^{*2} = A_e\int_{0}^{\infty}e^{\frac{\displaystyle m-\sqrt{p_T^{*2}+m^2}}{\displaystyle T_e}}{\rm d}p_T^{*2}\\
\nonumber &&z = \sqrt{p_T^{*2}+m^2} - m\\
\nonumber &&{\rm d}z = \frac{{\rm d}p_T^{*2}}{\sqrt{p_T^{*2}+m^2}} = \frac{{\rm d}p_T^{*2}}{m + z}\\
\nonumber &&(m+z){\rm d}z = {\rm d}p_T^{*2}\\
\nonumber &&A_e\int_{0}^{\infty}e^{\frac{\displaystyle m-\sqrt{p_T^{*2}+m^2}}{\displaystyle T_e}}{\rm d}p_T^{*2} = A_e\int_{0}^{\infty}e^{-\frac{\displaystyle z}{\displaystyle T_e}}2(m+z){\rm d}z = A_e(2mT_e + 2T_e^2).
\end{eqnarray}
\end{linenomath}
Therefore, the relative contribution $R$ can be expressed by the formula:
\begin{linenomath}
\begin{equation}
\label{eq.r}
R = \frac{AnT^2}{AnT^2 + A_e(2MT_e + 2T_e^2)(n-1)}.
\end{equation}
\end{linenomath}
In figure ~\ref{fig1} the parameters of the fit function and the relative contribution $R$ of the power-law type distribution to the charged particle production spectra (equation~(\ref{eq.r})) are shown as function of the charged particle rapidity ($\eta^*$). %This contribution is calculated from the H1 data fit to the function ~(\ref{eq.exppl}) according to the equation ~(\ref{eq.r}). 
Close to the virtual photon direction (large values of $\eta^*$) the $p_T^*$ spectrum can be described by a power-law term only, 
%One could observe that the particles produced in the photon fragmentation region at high rapidity values are described by the power-law statistical distribution alone. 
while at central rapidities the data require a significant exponential (Boltzmann-like) contribution. %for particles produced at central in the rapidity space. 
Moreover, the smaller $\eta^*$ the larger the exponential statistical contribution is required to describe the inclusive charged particle spectrum. Note, that in the $pp$ interaction at about the same collision energy as here for $\gamma^*p$ at HERA the data require only about $30\%$ of the power-law type contribution to the charged particle spectrum measured at central rapidities, while the residual $70\%$ of the particle spectrum is described by the exponential contribution~\cite{OUR1}. Thus, we observe that the particle production regime changes when particle rapidity values approach the proton hemisphere in the rapidity space of DIS events.


\section{Conclusion}
The first measurement of charged particle production spectra in $ep$ collisions at reduced proton beam energy $E_p = 460~$GeV with the H1 detector in the virtual photon-proton centre-of-mass frame was performed. The kinematic range of the analysis covers low photon virtualities, $5 < Q^2 < 10~$GeV$^2$,
and from medium to high values of inelasticit, y $0.35 < y < 0.8$. The double differential charged particle production cross sections ${{\rm d}^2\sigma}/{d{\rm p}^{*2}_T{\rm d}\eta^*}$ are measured in the pseudorapidity region $0 < \eta^* <3.5$ in seven equal bins. The measured transverse momentum distributions show different shape, depending on the $\eta^*$ value. The Monte Carlo models RAPGAP and DJANGOH describe the shape of the cross section in $\eta^*$ but both fail to describe shape of the cross section ${{\rm d}^2\sigma}/{d{\rm p}^{*2}_T{\rm d}\eta^*}$.
\par
In order to investigate the change in hadroproduction dynamics with $\eta^*$ the data are approximated by the recently introduced approach~(\ref{eq.exppl}). This parameterisation provides a much better description of the experimental data than those traditionally used. Moreover, the observed change in the particle production regime when particle rapidity values approach the proton hemisphere in the rapidity space of DIS events, is rather well explained by the newly introduced qualitative model~\cite{OUR2}.

% \noindent
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% (such as figure~\ref{fig:diff}, from~\cite{diff})
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\begin{thebibliography}{99}

\bibitem{OUR1}
  A.~A.~Bylinkin and A.~A.~Rostovtsev,
  ``Parametrization of the shape of hadron-production spectra in high-energy particle interactions,''
  Phys.\ Atom.\ Nucl.\  {\bf 75} (2012) 999
   [Yad.\ Fiz.\  {\bf 75} (2012) 1060].
  %%CITATION = PANUE,75,999;%%
\bibitem{H1particle}
C. Adloff et al. [ H1 Collaboration],
"Measurement of Charged Particle Transverse Momentum Spectra in Deep Inelastic Scattering",
Nucl.\ Phys.\ {\bf B 485} (1996)3 ;\\
C. Alexa {\it et al.} [ H1 Collaboration],
``Measurement of Charged Particle Spectra in Deep-Inelastic ep Scattering at HERA", submitted to 
 Eur.\ Phys.\ J.\ C, [arxiv:1302.1321].
\bibitem{FL}
  F.~D.~Aaron {\it et al.}  [ H1 Collaboration],
  ``Measurement of the Inclusive $e{\pm}p$ Scattering Cross Section at High Inelasticity y and of the Structure Function $F_L$,''
  Eur.\ Phys.\ J.\  {\bf C 71} (2011) 1579
  [arXiv:1012.4355].
  %%CITATION = ARXIV:1012.4355;%%

\bibitem{OUR2}
  A.~A.~Bylinkin and A.~A.~Rostovtsev,
  ``A photon-proton mariage,''
  arXiv:1209.0958 [hep-ph].
  %%CITATION = ARXIV:1209.0958;%%
  
\bibitem{old_model} R. Hagedorn, Riv. Nuovo Cim. {\bf 6} (1983) 1.

\end{thebibliography}

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\newpage
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\begin{figure*}[t]
\begin{center}
\includegraphics[width = 14cm]{h1prelim13-032f.eps}
\caption{\label{figeta} The measured differential $ep$ cross section ${\rm d}\sigma/{\rm d}\eta^*$ for inclusive production of charged particles. Particles with a $p^*_T > 0~$GeV are considered. The lines represent the normalized prediction of  DJANGOH and RAPGAP respectively.}
\end{center}
\end{figure*}

\begin{figure*}[hhh]

\quad
\includegraphics[width =7.5cm]{h1prelim13-032fFigures:.eps}
\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}

\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}
\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}

\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}
\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}

\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}
\quad

\caption{\label{figpt} The measured charged particle double differential cross section ${{\rm d}^2\sigma}/{d{\rm p}^2_T{\rm d}\eta}$  for seven $\eta*$ intervals together with DJANGOH and RAPGAP predictions.}
\end{figure*}

\begin{figure*}[hhh]

\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}
\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}

\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}
\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}

\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}
\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}

\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}
\quad

\caption{\label{fig.rat} The ratios of normalised MC over data using the same as used in figure~\ref{figeta} for seven $\eta*$ intervals.}
\end{figure*}

\begin{figure*}[hhh]

\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}
\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}

\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}
\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}

\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}
\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}

\quad
\includegraphics[width =7.5cm]{h1prelim13-032f.eps}
\quad

\caption{\label{fig} Double differential charged particle cross section ${{\rm d}^2\sigma}/{d{\rm p}^2_T{\rm d}\eta}$ for  seven $\eta*$ intervals together results from the fits of  the function~(\ref{eq.exppl}): the red  line shows the exponential term and the blue one - the power law.  Bin-center correction is performed.}
\end{figure*}



\begin{figure*}[hhh]
\includegraphics[width = 8cm]{h1prelim13-032f.eps}
\quad
\includegraphics[width = 8cm]{h1prelim13-032f.eps}
\quad

\includegraphics[width = 8cm]{h1prelim13-032f.eps}
\quad
\includegraphics[width = 8cm]{h1prelim13-032f.eps}
\quad

\caption{\label{fig1} Contribution $R$ of the power law term and fitted parameters of ~(\ref{eq.exppl}) as function of pseudorapidity ($\eta*$). The data points used for the fits included uncorrelated systematics.}

\end{figure*}
\end{document}




